PDLAED3(l) ) PDLAED3(l)NAME
PDLAED3 - find the roots of the secular equation, as defined by the
values in D, W, and RHO, between 1 and K
SYNOPSIS
SUBROUTINE PDLAED3( ICTXT, K, N, NB, D, DROW, DCOL, RHO, DLAMDA, W, Z,
U, LDU, BUF, INDX, INDCOL, INDROW, INDXR, INDXC,
CTOT, NPCOL, INFO )
INTEGER DCOL, DROW, ICTXT, INFO, K, LDU, N, NB, NPCOL
DOUBLE PRECISION RHO
INTEGER CTOT( 0: NPCOL-1, 4 ), INDCOL( * ), INDROW( * ),
INDX( * ), INDXC( * ), INDXR( * )
DOUBLE PRECISION BUF( * ), D( * ), DLAMDA( * ), U( LDU, *
), W( * ), Z( * )
PURPOSE
PDLAED3 finds the roots of the secular equation, as defined by the val‐
ues in D, W, and RHO, between 1 and K. It makes the appropriate calls
to SLAED4
This code makes very mild assumptions about floating point arithmetic.
It will work on machines with a guard digit in add/subtract, or on
those binary machines without guard digits which subtract like the Cray
X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on
hexadecimal or decimal machines without guard digits, but we know of
none.
ARGUMENTS
ICTXT (global input) INTEGER
The BLACS context handle, indicating the global context of the
operation on the matrix. The context itself is global.
K (output) INTEGER
The number of non-deflated eigenvalues, and the order of the
related secular equation. 0 <= K <=N.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
NB (global input) INTEGER
The blocking factor used to distribute the columns of the
matrix. NB >= 1.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, D contains the eigenvalues of the two submatrices to
be combined. On exit, D contains the trailing (N-K) updated ei‐
genvalues (those which were deflated) sorted into increasing
order.
DROW (global input) INTEGER
The process row over which the first row of the matrix D is dis‐
tributed. 0 <= DROW < NPROW.
DCOL (global input) INTEGER
The process column over which the first column of the matrix D
is distributed. 0 <= DCOL < NPCOL.
Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
On entry, Q contains the eigenvectors of two submatrices in the
two square blocks with corners at (1,1), (N1,N1) and (N1+1,
N1+1), (N,N). On exit, Q contains the trailing (N-K) updated
eigenvectors (those which were deflated) in its last N-K col‐
umns.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,NQ).
RHO (global input/output) DOUBLE PRECISION
On entry, the off-diagonal element associated with the rank-1
cut which originally split the two submatrices which are now
being recombined. On exit, RHO has been modified to the value
required by PDLAED3.
DLAMDA (global output) DOUBLE PRECISION array, dimension (N) A
copy of the first K eigenvalues which will be used by SLAED3 to
form the secular equation.
W (global output) DOUBLE PRECISION array, dimension (N)
The first k values of the final deflation-altered z-vector which
will be passed to SLAED3.
Z (global input) DOUBLE PRECISION array, dimension (N)
On entry, Z contains the updating vector (the last row of the
first sub-eigenvector matrix and the first row of the second
sub-eigenvector matrix). On exit, the contents of Z have been
destroyed by the updating process.
U (global output) DOUBLE PRECISION array
global dimension (N, N), local dimension (LDU, NQ). Q contains
the orthonormal eigenvectors of the symmetric tridiagonal matrix.
LDU (input) INTEGER
The leading dimension of the array U.
QBUF (workspace) DOUBLE PRECISION array, dimension 3*N
INDX (workspace) INTEGER array, dimension (N)
The permutation used to sort the contents of DLAMDA into ascend‐
ing order.
INDCOL (workspace) INTEGER array, dimension (N)
INDROW (workspace) INTEGER array, dimension (N)
INDXR (workspace) INTEGER array, dimension (N)
INDXC (workspace) INTEGER array, dimension (N)
CTOT (workspace) INTEGER array, dimension( NPCOL, 4)
NPCOL (global input) INTEGER
The total number of columns over which the distributed subma‐
trix is distributed.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute the ith eigenvalue.
ScaLAPACK version 1.7 13 August 2001 PDLAED3(l)
